Real time wave forecasting using neural networks

Forecasting of ocean wave heights, with warning time of a few hours or days, is necessary in planning many operation-related activities in the ocean. Such information is currently derived by numerically solving the differential equation representing wave energy balance. The solution procedure involved is extremely complex and calls for very large amounts of meteorological and oceanographic data. This paper presents a complementary and simple method to make a point forecast of waves in real time sense based on the current observation of waves at a site. It incorporates the technique of neural networks. The network involved is first trained by different algorithms and then used to forecast waves with lead times varying from 3 to 24 h. The results of different training algorithms are compared with each other. The neural output is further compared with the statistical AR models.     

Real-time wave forecasting using genetic programming

The forecasting of ocean waves on real-time or online basis is necessary while carrying out any operational activity in the ocean. In order to obtain forecasts that are station-specific a time-series-based approach like stochastic modeling or artificial neural network was attempted by some investigators in the past. This paper presents an application of a relatively new soft computing tool called genetic programming for this purpose. Genetic programming is an extension of genetic algorithm and it is suited to explore dependency between input and output data sets. The wave rider buoy measurements available at two locations in the Gulf of Mexico are analyzed. The forecasts of significant wave heights are made over lead times of 3, 6, 12 and 24 h. The sample size belonged to a period of 15 years and it included an extensive testing period of 5 years. The forecasts made by the approach of genetic programming indicated that it can be regarded as a promising tool for future applications to ocean predictions.     

Ocean wave forecasting using recurrent neural networks

The tremendous increase in offshore operational activities demands improved wave forecasting techniques. With the knowledge of accurate wave conditions, it is possible to carry out the marine activities such as offshore drilling, naval operations, merchant vessel routing, nearshore construction, etc. more efficiently and safely. This paper describes an artificial neural network, namely recurrent neural network with rprop update algorithm and is applied for wave forecasting. Measured ocean waves off Marmugao, west coast of India are used for this study. Here, the recurrent neural network of 3, 6 and 12 hourly wave forecasting yields the correlation coefficients of 0.95, 0.90 and 0.87, respectively. This shows that the wave forecasting using recurrent neural network yields better results than the previous neural network application.     

Neural networks for wave forecasting

The physical process of generation of waves by wind is extremely complex, uncertain and not yet fully understood. Despite a variety of deterministic models presented to predict the heights and periods of waves from the characteristics of the generating wind, a large scope still exists to improve on the existing models or to provide alternatives to them. This paper explores the possibility of employing the relatively recent technique of neural networks for this purpose. A simple 3-layered feed forward type of network is developed to obtain the output of significant wave heights and average wave periods from the input of generating wind speeds. The network is trained with different algorithms and using three sets of data. The results show that an appropriately trained network could provide satisfactory results in open wider areas, in deep water and also when the sampling and prediction interval is large, such as a week. A proper choice of training patterns is found to be crucial in achieving adequate training.     

Neural network for wave forecasting among multi-stations

Unlike in the open sea, the use of wind information for forecasting waves may encounter more ambiguous uncertainties in the coastal or harbor area due to the influence of complicated geometric configurations. Thus this paper attempts to forecast the waves based on learning the characteristics of observed waves, rather than the use of the wind information. This is reported in this paper by the application of the artificial neural network (ANN), in which the back-propagation algorithm is employed in the learning process for obtaining the desired results. This model evaluated the interconnection weights among multi-stations based on the previous short-term data, from which a time series of waves at a station can be generated for forecasting or data supplement based on using the neighbor stations data. Field data are used for testing the applicability of the ANN model. The results show that the ANN model performs well for both wave forecasting and data supplement when using a short-term observed wave data.     

Forecasting ocean waves: Comparing a physics-based model with statistical models

The literature on ocean wave forecasting falls into two categories, physics-based models and statistical methods. Since these two approaches have evolved independently, it is of interest to determine which approach can predict more accurately, and over what time horizons. This paper runs a comparative analysis of a well-known physics-based model for simulating waves near shore, SWAN, and two statistical techniques, time-varying parameter regression and a frequency domain algorithm. Forecasts are run for the significant wave height, over horizons ranging from the current period (i.e., the analysis time) to 15 h. Seven data sets, four from the Pacific Ocean and three from the Gulf of Mexico, are used to evaluate the forecasts. The statistical models do extremely well at short horizons, producing more accurate forecasts in the 1–5 hour range. The SWAN model is superior at longer horizons. The crossover point, at which the forecast error from the two methods converges, is in the area of 6 h. Based on these results, the choice of statistical versus physics-based models will depend on the uses to which the forecasts will be put. Utilities operating wave farms, which need to forecast at very short horizons, may prefer statistical techniques. Navies or shipping companies interested in oceanic conditions over longer horizons will prefer physics-based models.     

Interpolation of wave heights

Remote sensing of waves often necessitates presentation of data in the form of wave height values grouped over large time intervals. This restricts their use to long-term applications only. This paper describes how such data can be made suitable for short-term usage in the field. Weekly mean significant wave heights were derived from their monthly mean observations with the help of different alternative techniques. These include model-free neural network schemes as well as model-based statistical and numerical methods. Superiority of neural networks was noted when the estimations were compared with corresponding observations. The network was trained using three different training algorithms, viz., error back propagation, conjugate gradient and cascade correlation. The technique of cascade correlation took minimum training time and showed better coefficient of correlation between observations and network output.     

Wave group statistics from numerical simulations of a random sea

Two commonly used methods of simulating random time series, given a target power spectrum, are discussed. Wave group statistics, such as the mean length of runs of high waves, produced by the different simulation schemes are compared. The target spectra used are obtained from ocean measurements, and cover a wide range of ocean conditions. For a sufficiently large number of spectral components, no significant differences are found in the wave group statistics produced by the two simulation techniques.     

海浪破碎对海洋上混合层中湍能量收支的影响

海浪破碎产生一向下输入的湍动能通量,在近海表处形成一湍流生成明显增加的次层,加强了海洋上混合层中的湍流垂向混合。为了研究海浪破碎对混合层中湍能量收支的影响,文中分析了海浪破碎对海洋上混合层中湍流生成的影响机制,采用垂向一维湍封闭混合模式,通过改变湍动能方程的上边界条件,引入了海浪破碎产生的湍动能通量,并分别对不同风速下海浪破碎的影响进行了数值研究,分析了混合层中湍能量收支的变化。当考虑海浪破碎影响时,近海表次层中的垂直扩散项和耗散项都有显著的增加,该次层中被耗散的湍动能占整个混合层中耗散的总的湍能量的92.0%,比无海浪破碎影响的结果增加了近1倍;由于平均流场切变减小,混合层中的湍流剪切生成减小了3.5%,形成一种存在于湍动能的耗散和垂直扩散之间的局部平衡关系。在该次层以下,局部平衡关系与壁层定律的结论一致,即湍动能的剪切生成与耗散相平衡。研究结果表明,海浪破碎在海表产生的湍动能通量影响了海洋上混合层中的各项湍能量收支间的局部平衡关系。     

Linear irregular wave generation in a numerical wave tank

In the design of any floating or fixed marine structure, it is vital to test models in order to understand the fluid/structure interaction involved. A relatively inexpensive method, compared to physical model testing, of achieving this is to numerically model the structure and the wave conditions in a numerical wave tank. In this paper, a methodology for accurately replicating measured ocean waves in a numerical model at full scale is detailed. A Fourier analysis of the measured record allows the wave to be defined as a summation of linear waves and, therefore, Airy's linear wave theory may be used to input the wave elevation and associated water particle velocities. Furthermore, a structure is introduced into the model to display the ability of the model to accurately predict wave–structure interaction. A case study of three individual measured waves, which are recorded at the Atlantic marine energy test site, off the west coast of Ireland, is also presented. The accuracy of the model to replicate the measured waves and perform wave–structure interaction is found to be very high. Additionally, the absolute water particle velocity profile below the wave from the numerical model is compared to a filtered analytical approximation of the measured wave at a number of time-steps and is in very good agreement.     

Wave height forecasting in Dayyer, the Persian Gulf

Forecasting of wave parameters is necessary for many marine and coastal operations. Different forecasting methodologies have been developed using the wind and wave characteristics. In this paper, artificial neural network (ANN) as a robust data learning method is used to forecast the wave height for the next 3, 6, 12 and 24 h in the Persian Gulf. To determine the effective parameters, different models with various combinations of input parameters were considered. Parameters such as wind speed, direction and wave height of the previous 3 h, were found to be the best inputs. Furthermore, using the difference between wave and wind directions showed better performance. The results also indicated that if only the wind parameters are used as model inputs the accuracy of the forecasting increases as the time horizon increases up to 6 h. This can be due to the lower influence of previous wave heights on larger lead time forecasting and the existing lag between the wind and wave growth. It was also found that in short lead times, the forecasted wave heights primarily depend on the previous wave heights, while in larger lead times there is a greater dependence on previous wind speeds.     

A discrete correction scheme for envelope approach of wave group statistics

The existence of empty envelope excursions (EEE) brings error to the envelope approach of wave group statistics, which identifies wave group by envelope upcrossing of a critical level. A group number correction scheme is suggested in this paper to exclude EEE from wave group statistics. To this end, the Ditlevson and Lindgren [J. Sound Vib. 122 (1988) 571] theory about the fraction of empty excursion envelopes (FEEE) is examined to see if it fits for ocean waves. The sea waves are simulated with Monte Carlo method and with P-M and JONSWAP spectrums. The values of FEEE of the simulated waves are investigated and compared with the theory of Ditlevson and Lindgren. The comparison shows that, at the second-order approximation, theoretical predictions of FEEE are close to those derived from simulations. This approximate analytical expression of FEEE is then employed to form a group number correction scheme. Comparisons between numerical and theoretical results of wave group properties show that this correction scheme is quite effective.     

珠江口近海海域海浪预报方法研究

根据珠江口近海海域的风区和水深等特点,将该海域划分为4个区域,结合港口规范方法、SMB 方法、适用于深浅水的风浪要素计算方法、原苏联预报模式以及莆田海堤试验站方法等 5 种风浪经验预报模式,对该海域 2004～2005 年的风浪进行后报、检验和订正,总结出对应不同区域最适合的风浪预报方法.     

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.     

Forecasting ocean wave energy: Tests of time-series models

This paper evaluates the ability of time-series models to predict the energy from ocean waves. Data sets from four Pacific Ocean sites are analyzed. The energy flux is found to exhibit nonlinear variability. The probability distribution has heavy tails, while the fractal dimension is non-integer. This argues for using nonlinear models. The primary technique used here is a time-varying parameter regression in logs. The time-varying regression is estimated using both a Kalman filter and a sliding window, with various window widths. The sliding window method is found to be preferable. A second approach is to combine neural networks with time-varying regressions, in a hybrid model. Both of these methods are tested on the flux itself. Time-varying regressions are also used to forecast the wave height and wave period separately, and combine the forecasts to predict the flux. Forecasting experiments are run at an hourly frequency over horizons of 1-4 h, and at a daily frequency over 1-3 days. All the models are found to improve relative to a random walk. In the hourly data sets, forecasting the components separately achieves the best results in three out of four cases. In daily data sets, the hybrid and regression models yield similar outcomes. Because of the intrinsic variability of the data, the forecast error is fairly high, comparable to the errors found in other forms of alternative energy, such as wind and solar.     

Analysis of freak wave measurements in the Sea of Japan

This paper presents an analysis of a set of available freak wave measurements gathered from several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan. The analysis provides an ideal opportunity to catch a glimpse of the statistics of freak waves in the ocean. The results show that a well-defined freak wave may occur in the developed wind–wave condition: S(f)∝f⁻⁴, with single-peak directional spectra. The crest and trough amplitude distributions of the observed sea waves including freak waves are different from the Rayleigh distribution, although the wave height distribution tends to agree with the Rayleigh distribution. Freak waves can be readily identified from the wavelet spectrum where a strong energy density occurs in the spectrum, and is instantly surged and seemingly carried over to the high-frequency components at the instant the freak wave occurs.     

Ocean wave transmission by submerged reef—A physical model study

Ocean waves can be destructive as steeper waves due to their high energy eroding the sandy beaches. During storm surge or high tide, the water level rises and if large waves occur, they will break closer to the beach, releasing enormous amount of energy resulting in strong currents. This causes heavy loss of beach material due to large-scale erosion. If these waves are made to break prematurely and away from the beach, they can be attenuated so as to reduce beach erosion. The reef, which is a homogeneous pile of armour units without a core, breaks the steeper ocean waves, dissipates a major portion of their energy and transmits attenuated waves. This paper experimentally investigates the armour stone stability of the submerged reef and the influence of its varying distance from shore and crest width on ocean wave transmission.     

Exact asymmetric slope distributions in stochastic Gauss–Lagrange ocean waves

The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. This paper presents exact slope distributions and other characteristic distributions at level crossings for symmetric and asymmetric Lagrange space and time waves. These distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are: slopes obtained by asynchronous sampling in space or time, slopes in space or time, and horizontal particle velocity, when waves are observed when the water level crosses a predetermined level.     

Numerical modelling of liquefaction in loose sand deposits subjected to ocean waves

The failure of marine structures is often attributed to liquefaction in loose sand deposits that are subjected to ocean waves. In this study, a two-dimensional integrated numerical model is developed to characterize the liquefaction behaviours of loosely deposited seabed foundations under various types of ocean waves. In the present model, Reynolds-Averaged Navier–Stokes (RANS) equations are used to simulate the surface wave motion, and Biot's consolidation equations are used to link the solid-pore fluid interactions in a porous medium. A poro-elasto-plastic solution is used to reproduce foundation behaviour under cyclic shearing. Unlike previous investigations, both oscillatory and residual soil responses were considered; they are coupled in an instantaneous approach. Verification of the model results to the previous centrifugal wave tests is carried out, obtaining fairly good agreement. Numerical examples show that foundation behaviour under various types of wave loading, particularly standing waves or a solitary wave, embodies a completely two-dimensional process in terms of residual pore pressure development. The parametric studies demonstrate that liquefaction caused by the build-up of pore pressures is more likely to occur in loosely deposited sand foundations with poor drainage and under large waves.